Asymptotic solvers for ordinary differential equations with multiple frequencies Articles uri icon

publication date

  • November 2015

start page

  • 2279

end page

  • 2300


  • 11


  • 58

International Standard Serial Number (ISSN)

  • 1674-7283

Electronic International Standard Serial Number (EISSN)

  • 1869-1862


  • We construct asymptotic expansions for ordinary differential equations with highly oscillatory forcing terms, focusing on the case of multiple, non-commensurate frequencies. We derive an asymptotic expansion in inverse powers of the oscillatory parameter and use its truncation as an exceedingly effective means to discretize the differential equation in question. Numerical examples illustrate the effectiveness of the method.


  • oscillator; van